10,770 research outputs found
Another Correction. Error estimates for Binomial approximations of game options
The Annals of Applied Probability 16 (2006) 984--1033 [URL:
http://projecteuclid.org/euclid.aoap/1151592257]Comment: Published in at http://dx.doi.org/10.1214/07-AAP479 the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Using schedulers to test probabilistic distributed systems
This is the author's accepted manuscript. The final publication is available at Springer via http://dx.doi.org/10.1007/s00165-012-0244-5. Copyright Ā© 2012, British Computer Society.Formal methods are one of the most important approaches to increasing the confidence in the correctness of software systems. A formal specification can be used as an oracle in testing since one can determine whether an observed behaviour is allowed by the specification. This is an important feature of formal testing: behaviours of the system observed in testing are compared with the specification and ideally this comparison is automated. In this paper we study a formal testing framework to deal with systems that interact with their environment at physically distributed interfaces, called ports, and where choices between different possibilities are probabilistically quantified. Building on previous work, we introduce two families of schedulers to resolve nondeterministic choices among different actions of the system. The first type of schedulers, which we call global schedulers, resolves nondeterministic choices by representing the environment as a single global scheduler. The second type, which we call localised schedulers, models the environment as a set of schedulers with there being one scheduler for each port. We formally define the application of schedulers to systems and provide and study different implementation relations in this setting
Oscillating behaviour of the spectrum for a plasmonic problem in a domain with a rounded corner
We investigate the eigenvalue problem in a 2D domain divided into two regions
. We are interested in situations where takes positive
values on and negative ones on . Such problems appear
in time harmonic electromagnetics in the modeling of plasmonic technologies. In
a recent work [15], we highlighted an unusual instability phenomenon for the
source term problem associated with : for certain
configurations, when the interface between the subdomains
presents a rounded corner, the solution may depend critically on the value of
the rounding parameter. In the present article, we explain this property
studying the eigenvalue problem . We provide an asymptotic
expansion of the eigenvalues and prove error estimates. We establish an
oscillatory behaviour of the eigenvalues as the rounding parameter of the
corner tends to zero. We end the paper illustrating this phenomenon with
numerical experiments.Comment: Mathematical Modelling and Numerical Analysis (ESAIM: M2AN),
09/12/2016. arXiv admin note: text overlap with arXiv:1304.478
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